Non-singular boundary integral methods for fluid mechanics applications

Abstract

A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad applicability of the approach is illustrated with a number of problems of practical interest to fluid and continuum mechanics including the solution of the Laplace equation for potential flow, the Helmholtz equation as well as the equations for Stokes flow and linear elasticity.

Cited by in corpus (19)

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• Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
• Stokesian dynamics of pill-shaped Janus particles with stick and slip boundary conditions
• Boundary regularized integral equation formulation (BRIEF) of Stokes flow
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• Kernel Free Boundary Integral Method for 3D Stokes and Navier Equations on Irregular Domains
• A robust and accurate formulation of molecular and colloidal electrostatics
• Helmholtz Decomposition and Boundary Element Method applied to Dynamic Linear Elastic Problems
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• Helmholtz equation and non-singular boundary elements applied to multi-disciplinary physical problems
• New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow
• A non-singular boundary element method for interactions between acoustical field sources and structures